Plot samples points in the domain and tries to make a curve out of it. For tens of sample points,
Plot[(Sin[t]), {t, -30, 10000}]
is going to oscillate so many times that the sampled points have nearly random y values.

If you sample at more points,
Plot[(Sin[t]), {t, -30, 10000}, PlotPoints->1000]
then a finite-width curve will make a blue rectangle.

Do you want to view the curve at high x values?
Plot[(Sin[t]), {t, 10000-30, 10000} ]